Effect size for ANCOVA

We begin by considering various measurements of effect size for Example 1 of Basic Concepts of ANCOVA (using the results of the analysis as summarized in Figure 3 of Regression Approach to ANCOVA).

A commonly used measure of effect size, despite it being positively biased, is eta squared, η2, which is simply r2.  For Example 1 of Basic Concepts of ANCOVA,

Eta squared ANCOVAAnother commonly used measure of effect size is partial η2 = \frac{SS_{Treat}}{SS_{Tot}+SS_{Res}} which for Example 1 of Basic Concepts of ANCOVA is

Partial eta squared ANCOVA

We can also use these measures of effect size for the covariate.

Effect size covariate

This shows that the covariate explains a larger part of the variance (either total or unattributed to other variables) than the method.

For the contrasts we can use the usual measure r = \sqrt{\frac {t^2}{t^2+df}}. For the comparison in Example 1 of Contrasts for ANCOVA, we have

Effect size contrast ANCOVA

which is a relatively large effect.

We can also compute the effect size of the covariate using the regression coefficient information in Figure 5 of Regression Approach to ANCOVA (cell U36), and see that it is a very large effect.

image2592Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Howell, D. C. (2010) Statistical methods for psychology (7th ed.). Wadsworth, Cengage Learning.
https://labs.la.utexas.edu/gilden/files/2016/05/Statistics-Text.pdf

Hedges, L. V., Tipton, E., Zejnullahi, Diaz, K. G. (2023) Effect sizes in ANCOVA and difference-in-differences designs

7 thoughts on “Effect size for ANCOVA”

  1. Hello,
    I want to echo the thanks for this great resource.

    I am running the ACNOVA on 4 categories, and want to be able to tell if the categories are different from each other (or what categories are statistically similar to one another)

    I am able to run your tool to get the SS, slope, adj mean, and determine the r^2 for each treatment. Is is possible to use this analysis to determine if the categories are statistically different or similar to one another?

    Thanks, and happy to clarify,
    Rob

    Reply

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